These notebooks present experiments using a transportation distance between GMM defined by restricting the set of possible coupling measures to Gaussian mixtures, described in:

Delon, Desolneux, A Wasserstein-type distance in the space of Gaussian Mixture Models, 2019

See also :

Chen, Georgiou, Tannenbaum, Optimal transport for Gaussian mixture models, 23rd International Symposium on Mathematical Theory of Networks and Systems, 2018